You can create an attribute and put it in the button's label. This way, you can simply modify the attribute's value in the js, and it will change in the button as well.
Component:
<aura:attribute name="buttonLabel" type="String" default="Get password" />
<ui:button aura:id = "Btn1" label="{!v.buttonLabel}" class="slds-button slds-button_brand" press="{!c.handleClick}" />
Controller.js
component.set("v.buttonLabel", "New label");